Question

Escreva na forma de a+bi:
(2-3i)⁵

Answer 1

a+bi:

(2-3i)⁵ = 2^5 + 2^4.(-3i) + 2^3.(-3i)^2 + 2^2.(-3i)^3 + 2^1.(-3i)4 + (-3i)^5

(2-3i)⁵ = 32 + 16.(-3i) + 8.9i^2 + 4.(-27i^3) + 2.(+81i^4)  + (-243i^5)

(2-3i)⁵ = 32 - 48i + 72(-1) - 108(- i ) + 162(+1) - 243(-i)

(2-3i)⁵ = 32 - 48i - 72 + 108i + 162 + 243i

(2-3i)⁵ = 32 - 72 + 162 - 48i + 108i + 243i

(2-3i)⁵ = 122 - 303i 

a + bi = 122 - 303i    ===> a = 122     ; b = - 303